GROUND-STATES OF TWO DIRECTED POLYMERS

Joint ground states of two directed polymers in a random medium are investigated. Using exact min-cost flow optimization, the true two-line ground-state is compared with the single line ground state plus its first excited state with "worst-possible" initial conditions, where the two lines start next to each other. It is found that these two-line configurations are (for almost all disorder configurations) distinct implying that the true two-line ground-state is nonseparable, which means that the two-line ground state cannot be obtained by adding a second line to the first line in the one-line ground state without deforming the first line. The effective interaction energy between the two lines scales with the system size with the scaling exponents 0.39 ± 0.03 and 0.21 ± 0.02 in 2D and 3D, respectively.